Reflectivity and Braggs Wavelength in FBG

Dinesh Arora, Dr.Jai Prakash, Hardeep Singh & Dr.Amit Wason
341International Journal of Engineering (IJE), Volume (5) : Issue (5) : 2011
Reflectivity and Braggs Wavelength in FBG
Dinesh Arora ecedinesh@rediffmail.com
Research Scholar (ECE), Singhania University,
Jhunjhunu, Rajasthan-333515, INDIA
Dr. Jai Prakash ecedinesh@rediffmail.com
Professor in Department of Applied Physics,
Indo Global College of Engineering,
Mohali, Punjab-140109, INDIA
Hardeep Singh*
hardeep_saini17@yahoo.co.in
Associate Professor in Department of ECE,
Indo Global College of Engineering,
Dr.Amit Wason wasonamit13@gmail.com
Professor in Department of ECE,
Rayat & Bahra Institute of Engineering & Bio-Technology,
Abstract
We have presented an analytical model of splitters based on Fiber Bragg Grating used to detect a Bragg
wavelength from the number of wavelengths which are traveling in an optical fiber. The number of grids
and grating length can be used as a wavelength shifter. This paper presents experimental results that are
used to show the effect of number of grids, the length of the grating on the Bragg wavelength and
reflectivity of Fiber Bragg Grating (FBG). The pitch of grating is directly proportional to the grating length
and inversely proportional to number of grids. When the grating length is fixed and the number of grids is
increased, the Bragg wavelength decreases resulting in increased reflectivity. This increased reflectivity is
very small. Further when the number of grids is kept constant and the grating length is increased the
Bragg wavelength increases. The effect of this increase in grating length on reflectivity is a very small. In
our model, the effectiveness of the grating in extracting the Braggs wavelength is nearly 100%.
Keywords- Fiber Bragg Grating, Bragg Wavelength, Reflection, Number of Grids, Grating length, Pitch
1. INTRODUCTION
With the rapid growth of the Internet, capacity requirement is increasing day by day. This increase in the
requirement of capacity can be easily met by the existing optical fiber communication technology. The
transmission properties of an optical wave-guide are dictated by its structural characteristics, which have
a major effect in determining how an optical signal is affected as it propagates along the fiber [1]. Light
propagation occurs in the guiding region of waveguide on principle of total internal reflection at the
material interfaces. For this to occur, the guiding region must have a refractive index of greater value
than the materials surrounding it.
1.1 Fiber Bragg Grating
The Fiber Bragg Grating (FBG) was initially demonstrated by Ken Hill., K.O. [2]. FBG is a periodic
perturbation of the refractive index along the fiber length in the fiber’s core which is formed by exposure of
the core to an intense optical interference pattern. Germanium, a dopant used in many optical fiber cores,
is photosensitive to Ultraviolet (UV) light. A grating is a selective wavelength filter in the core of an optical
fiber. It is made by exposing a section of the fiber to UV light through a phase mask. An interference
pattern of maxima and minima is formed causing a permanent periodic change to the index of the core. A

small amount of light is reflected at each index variation. At the "center wavelength” or “Bragg
wavelength,” all the reflections add coherently. The grating reflects light in a narrow wavelength range,
centred at the so-called Bragg wavelength.
1.1.1 Grating Fabrication Technique
Many techniques have been developed for the fabrication of FBG i.e. transverse holographic (G.Meltz,
1989), phase mask (K.O.Hill, 1993) and point-by-point techniques [3]. When UV light radiates on an
optical fiber, the refractive index is changed permanently; this effect is known as ‘photosensitivity.’ Out of
these three, the phase mask is the most common technique due to its simple manufacturing process,
great flexibility and high performance.
Transverse holographic technique: The light from an UV source is split into two beams that are brought
together so that they intersect; the intersecting light beams form an interference pattern that is focused
using cylindrical lenses on to the core of optical fiber [3]. The fiber cladding is transparent to UV light,
whereas the core absorbs the light strongly. Due to this light beam the core is irradiated from the side,
thus giving rise to its name transverse holographic techniques. The holographic technique for grating
fabrication has two principal advantages.
• Bragg gratings could be photo imprinted in the core without removing the glass cladding.
• The period of the induced grating depends on the angle between the two interfering coherent UV
light beams.
Phase Mask Technique: In this technique the phase mask is placed between the UV light source and the
optical fiber. The shadow of the phase mask then determines the grating structure based on the
transmitted intensity of light striking the fiber [4] & [5].
FIGURE1: Phase mask fabrication techniques of Grating
Point-by-Point technique: In this technique each index perturbation is written point by point. Here, the
laser has a narrow beam that is equal to the grating period. This method of FBG inscription deep gratings
have been written in a range of optical fibers at arbitrary wavelengths. It can be used to write gratings with
periods of approximately 1 µm and above in a range of optical fibers [5]. In point by point technique, a
step change of refractive index is induced along the core of the fiber at a time. A single pulse of the UV
light passes through a mask to the core of the fiber containing a slit and thus the refractive index ( ) of the
corresponding core section increases locally. The fiber is then translated through a distance
corresponding to the grating pitch ( ) in parallel direction to the fiber axis, this process is repeated to form
the grating structure in the fiber core.
1.1.2 Grating Structure

The structure of the FBG can vary via the refractive index, or the grating period. The grating period can
be either uniform or graded or localized and distributed in a superstructure. The refractive index profile in
FBG can be uniform or apodized, and the refractive index offset is positive or zero. There are six common
structures for FBGs;
•Uniform positive-only index change,
•Gaussian apodized,
•Raised-cosine apodized,
•Chirped,
•Discrete phase shift, and
•Superstructure.
1.1.3 Grating Principle
When light passes through the FBG, the narrowband spectral component at the Bragg wavelength is
reflected by the FBG. The Bragg wavelength is given by the Equation (1) [6].
(1)
Where and Λ are the effective refractive index of the fiber and the pitch of the grating respectively.
Parameters of FBG, such as period of refractive index perturbation, magnitude of refractive index, grating
length and numbers of grids, give optical properties of FBG.
2. LITERATURE SURVEY
M.S. Ab-Rahman, et al. [7], investigated the effect of the refractive index of cladding ( ) to the Bragg
wavelength and reflectivity of the grating. They found that the effect of the was not linear. The Bragg
wavelength shifted periodically with the change of . The power also varied in a quadratic manner with
a change of . D.W. Huang, et al. [8], worked on reflectivity-tunable FBG reflector with acoustically
excited transverse vibration of the fiber. They observed that when the transverse vibration induced the
coupling between the core and cladding, the Bragg reflectivity varied from its original value to zero. With
this technique, they varied the Bragg reflectivity after a fiber grating was fabricated. C.Caucheteur,
et al. [9], investigated the polarization properties of Bragg grating. They concluded that FBGs prepared by
high-intensity laser pulse were characterized by high value polarization-dependent loss (PDL) and
differential group delay (DGD). F.Z.Zhang, et al. [10], examined the effect of the zero
th
-order diffraction of
the phase masks on FBG in polymer optical fiber by observing and analysing the micrographs of the
grating. When the strain was larger than 2%, the viscoelasticity of the polymer fiber was noticed. The 60
nm Bragg wavelength shift was observed when they investigated the strain response by stretching the
polymer optical fiber up to 6.5%.of the polymer optical fiber. B.A.Tahir, et al. [11], described the FBG
sensing system for strain measurement. They calculated the reflectivity by keeping the grating length
constant and varying the index modulation amplitude of the Grating. In their model, the average
reflectivity was 96% and negligible change in reflectivity was observed by variation in index modulation.
Also, if applied strain was uniform then Bragg wavelength shift occurred without modification of initial
spectrum shape. Good linear response was observed between applied strain and Bragg wavelength shift.
F.Zeng, et al. [12], proposed an approach to implement optical microwave filters using an FBGS with
identical reflectivity. The spectrum profile of the broadband light source can be controlled using an optical
filter, which could be used to control the filter coefficients to suppress the filters side-lobes. M.ANDO,
et al. [13], 2004, investigated the dependence of FBG characteristics on grating length. They concluded
that under the standard FBG fabrication condition, the exposure time of the FBG to excimer laser
irradiation for a given transmission time was inversely proportional to the length of the grating. During
their investigation, they fixed the value of amplitude of refractive index modulation of the grating even
when the length was varied. S.Ugale, et al. [14], found that the reflectivity increases with increase in
grating length as well as index difference.

3. ANALYTICAL MODEL
In this paper, we have investigated the effect of number of grids and grating length which will be useful in
designing the wavelength splitter with the help of FBG. The Analytical model has been proposed for the
reflectivity of grating which is given by Equation (2).
(2)
Where ‘l’ is the length of the grating, ‘k’ is the coupling coefficient; δ is detuning factor and is the
detuning ratio. The detuning parameter for FBG of period is , is known as pitch or grating
period as in Equation (3).
(3)
N is number of grids or number of grating periods. Pitch of grating also depends upon the value of
effective refractive index and Brag wavelength as shown in Equation (4).
(4)
For sinusoidal variation in index perturbation, the coupling co-efficient for 1st order Bragg grating is
where is overlap integral between forward and reverse propagating mode. V is normalized frequency as
given in Equation (5).
(5)
Where
• is effective refractive index
• is radius of core
• is index difference
4. SIMULATION, RESULT & DISCUSSION
The work was carried out on Software MATLAB 7.2 of Mathworks. The analytical model thus constructed
has investigated with variation of some of the design parameters of FBG. We have fixed some of the
parameters i.e. index difference between core and cladding, radius of core and index amplitude of the
grating. As per Equation (5), the pitch of grating is inversely proportional to the number of grids and
directly proportional to grating length. Moreover, the number of grids also affects the reflectivity of grating.
Table1. shows the relation between the number of grids and Braggs wavelength. Moreover, with the
increase in number of grids, there is a negligible increase in reflectivity.

1.549 1.55 1.551 1.552 1.553 1.554
x 10
-6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wavelength
Reflectivity
Bragg Wavelength varying with number of Grids
N=5605
N=5608
N=5612
FIGURE 2: Bragg wavelength varying with number of grids of Grating N=5605, 5608 and 5612
1.542 1.544 1.546 1.548 1.55 1.552 1.554
x 10
-6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wavelength
Reflectivity
Bragg Wavelength varying with number of Grids
N=5615
N=5620
N=5625
FIGURE 3: Bragg wavelength varying with number of grids of Grating N=5615, 5620 and 5625

1.54 1.545 1.55 1.555 1.56 1.565
x 10
-6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wavelength
Reflectivity
Bragg Wavelength varying with FBG length
l=2.99mm
l=3.0mm
l=3.02mm
FIGURE 4: Bragg wavelength varying with Grating length =2.99mm, 3.00mm and 3.02mm
1.56 1.565 1.57 1.575 1.58 1.585 1.59
x 10
-6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wavelength
Reflectivity
Bragg Wavelength varying with FBG length
l=3.03mm
l=3.04mm
l=3.06mm
FIGURE 5: Bragg wavelength varying with Grating length =3.03mm, 3.04mm and 3.06mm
The results shown in Figure 2 and Figure 3 depict the reflectivity and Bragg wavelength variation with the
number of grids. It has been shown in Figure 2 also, that the Bragg wavelength varies with the number of

grids and it decreases with the increase in number of grids. Bragg wavelength was calculated to be
1552nm for 5605 number of grids, when grating length was fixed at 3mm. It was found that the Braggs
wavelength decreased with the increase in number of grids. It decreased to 1551nm and 1550nm when
the effective number of grids was increased to 5608 and 5612. For a fix value of grating, there is no
change in Reflectivity with the increase in the number of grids. In Figure 3 the results show that Bragg
wavelength of the grating was calculated to be 1549 for the number of grids as 5615, which was
decreased to 1548, 1547, when the number of grids of grating was increased to 5620 and 5625
respectively. Moreover, with the increase in the number of grids, there was a little increase in the
reflectivity of FBG. The reflectivity was increased to 99.65% with 5650 grids when the grating length was
3mm and to 99.61% for number of grids up to 5612.
N(Number of Grids) Bragg Wavelength(nm) Reflectivity (%)
5605 1552 99.61
5608 1551 99.61
5612 1550 99.61
5615 1549 99.62
5620 1548 99.62
5625 1547 99.63
5640 1545 99.63
5650 1540 99.65
TABLE 1: Characteristics of FBG with the Variation of number of Grids
Now, on same model of FBG splitter, we have fixed the number of grids (N) and studied the effect of
varying grating length on Bragg wavelength and reflectivity. As per Equation (3), the pitch of
grating is directly to the grating length. In this section, the number of Grids (N) is fixed at 5605 and the
grating length is varied to observe the effect on Bragg wavelength and reflectivity of the grating.
Grating length(mm) Bragg Wavelength(nm) Reflectivity (%)
2.99 1547 99.6
3.00 1552 99.6
3.02 1563 99.59
3.03 1568 99.58
3.04 1573 99.58
3.05 1583 99.56
3.06 1599 99.52
3.07 1630 99.45
TABLE 2: Characteristics of FBG with the Variation of Grating length
In Figure 5, the Bragg wavelength calculated was 1568 nm for 3.03mm grating length. With increase in
the grating length, the pitch of grating increased but the Bragg wavelength of the FBG decreased and at
the same time the reflectivity of the FBG also decreased. For the grating length of 3.04mm and 3.06mm,
the Bragg wavelength noted was 1573 nm and 1583nm respectively. The Table 2 also showed that for

increase of 0.02mm in the grating length, the Bragg wavelength shifted from 1573nm to 1583nm. The
reflectivity also decreased with the increase in grating length. It was 99.60 % for 2.99mm grating length
and 99.45% for 3.15mm grating length.
The experimental results show the effect of number of grids, the length of the grating on the Bragg
wavelength and reflectivity of FBG. It is clear that the pitch of grating is directly proportional to the grating
length and inversely proportional to number of grids. When the grating length is fixed and the number of
grids is increased, the Bragg wavelength decreases resulting in increased reflectivity. This increased
reflectivity is very small. Further when the number of grids is kept constant and the grating length is
increased the Bragg wavelength increases. The effect of this increase in grating length on reflectivity is a
very small. The effectiveness of the grating in extracting the Braggs wavelength is nearly 100%.
6. CONCLUSION
In our work, we have analyzed the effect of number of grids and grating length of FBG on reflectivity and
Bragg wavelength by keeping other parameters constant. The pitch of grating is directly proportional to
grating length and inversely proportional to number of grids. On increasing the number of grids, keeping
the grating length as fixed, the Bragg wavelength decreases and at the same time, the reflectivity
increases. The reflectivity increases by 0.02% with increase in the number of grids by 25 and at the same
time, Bragg wavelength shifted by 7nm. Also, when the grating length is varied by 0.02mm, keeping the
number of grid constant, the Bragg wavelength shifts by 10nm and reflectivity decreases by 0.02%. The
effectiveness of the grating in extracting the Braggs wavelength is nearly 100%.
7. REFERENCES
[1]. G.Keiser, “Optical Fiber communication”, Second Edition, Singapore, McGraw-Hill series in
Electrical Engineering, 1991.
[2]. K.O.Hill, Y.Fujii, and D.C.Johnson, “Photosensitivity in optical fiber waveguides: Application to
reflection filter fabrication”, Applied Physics Letters, VOL. 32, 647-649, 1978.
[3]. Z.Zhou, T.W. Graver, L. Hsu and J.Ou, “Techniques of Advanced FBG sensor: fabrication,
demodulation, encapsulation and their application in the structural health monitoring of Bridges”,
Pacific Science Review, VOL.5, 116-121, 2003.
[4]. K.O.Hill, and G. Meltz, “Fiber Bragg Grating Technology Fundamentals and Overview”, Journal
of Light wave technology, VOL. 15, NO.8, 1997.
[5]. G.D.Marshall, M. Arms and M.J. Withford, “Point by point femtosecond laser inscription of fiber
and waveguide Bragg grating for photonic device fabrication”, Proceeding of the 2nd Pacific
international conference on Application of Lasers and optics, 2006.
[6]. Z.Zhou and J.Ou, “Techniques of temperature compensation for FBG strain sensors used in
long-term structural monitoring”, Proceeding of Asian pacific fundamental problems of Opto- and
Microelectronics (APCOM 2004) Russia, 465-471, 2004.
[7]. M.S.Ab-Rahman and M.Fauzi, “Effect of Refractive index of cladding on Bragg wavelength and
reflection –the Application”, Australian Journal of Basic and Applied Science, VOL.3, NO.3, 2876-
2882, 2009.
[8]. D.W.Huang, W.F.Liy, C.W. Wu and C.C.Yang, “Reflectivity Tunable fiber Bragg Grating
Reflectors”,IEEE Photonics Technology letters, VOL.12, NO.2, 2000.
[9]. C.Caucheteur, P. Megret, T. Ernst and D.N.Nikogosya, “Polarization properties of FBG inscribed
by high intensity femtosecond 264 nm pulses”, Science Direct, Optical Communication 271, 303-
308, 2007.

[10]. F.Z. Zhang, C. Zhang and M.T.Xiao, “Inscription of polymer Optical Fiber Bragg grating at 962
nm and its potential in strain sensing”, IEEE photonics technology letters, VOL.22, NO.21, 2010.
[11]. B.A.Tahir, J. Ali and R.A.Rahman, “Strain measurement using FBG sensor”, American
Journal of Applied Science (special Issue), 40-48, 2005.
[12]. F.Zeng and J.Yao, “All optical microwave filters using uniform FBG with Identical Reflectivity”,
Journal of Lightwave Technology, VOL.23, NO.3, 2005.
[13]. M.Ando, M.Yamauchi, K.Nakayama, K. Moriyama and Y.Masuda, “Dependence of FBG
Characteristics on its Length”, Japanese Journal of Applied Physics, VOL.43, NO.7A, 4234-
4235, 2004.
[14]. S.Ugale and V.Mishra, “Fiber Bragg Grating modeling”, Characterization and Optimization with
different index profiles”, International Journal of Engineering Science and Technology, VOL.2,
NO. 9, 4463- 4468, 2010.

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